I'm teaching myself some physics, and I am having some difficulty with the concept of drift speed. My book derived the time between collisions using ma=Eq and then substituting the acceleration into the first equation of kinematics and solving for v(final) as the drift speed. The time it took for the average velocity to increase from zero to the drift speed was equal to the time between collisions. My question is: Why do the electrons cease to accelerate above the drift speed? I am aware that the drift speed is an average, but it seems like a constant emf in a circuit would cause the average velocity to gradually grow. Even if each elastic collision resets the velocity of the progenitor electron to zero, it seems that, with a constant field, eventually the circuit "runs out" of electrons traveling below the drift speed. So, why don't the electrons keep accelerating in a circuit? Thank you very much for any help.